Linear readout of integrated interferometric biosensors using a periodic wavelength modulation

An all‐optical phase modulation method for the linear readout of integrated interferometric biosensors is demonstrated, merging simple intensity detection with the advantages offered by spectral interrogation. The phase modulation is introduced in a simple and cost‐effective way by tuning a few nanometers the emission wavelength of commercial laser diodes, taking advantage of their well‐known drawback of power–wavelength dependence. The method is applied to the case of a bimodal waveguide (BiMW) interferometric biosensor, fabricated with standard silicon technology and operated at visible wavelengths, rendering a detection limit of 4×10−7 refractive index units for bulk sensing. The biosensing capabilities of the phase‐linearized BiMW device are assessed through the quantitative immunoassay of C‐reactive protein, a key protein in inflammatory processes. This method can be applied to any modal interferometer.


Introduction
Integrated optics-based biosensors are highly sensitive analytical platforms as required in clinical, pharmaceutical, or industrial fields. They offer compelling advantages such as label-free detections, reduction of sample and reagent volume, and very small dimensions which allow easy multiplexing and large-scale production, resulting in a reduced cost of the final product. Among them, interferometric arrangements have demonstrated the highest sensitivity, with detection limits in the range 10 −8 -10 −7 refractive index units (RIU) for bulk detection and fractions of pg/mm 2 for surface sensing [1,2].
The most commonly employed configurations are based on two-path arrangements such as Mach-Zehnder [3,4], Young [5][6][7], or Hartman interferometers [8,9], where the interference between the two propagating beams is recorded either as an intensity variation or as a displacement of the interference pattern.
As an alternative to double-path interferometers, singlepath configurations offer simplified fabrication and compact footprint, since the necessity of lateral beam splitting and recombination is suppressed. In the general scheme, two modes of different order or polarization propagate in the same channel. They both probe the sample solution but with different sensitivities, a consequence of their distinct confinement factors. The resulting relative phase difference can be evaluated as a variation of the far-field pattern created at the device output or as an intensity variation by Nanobiosensors and Bioanalytical Applications Group, Institut Català de Nanociència i Nanotecnologia (ICN2), CSIC & CIBER-BBN, 08193, Bellaterra, Barcelona, Spain * Corresponding author: e-mail: laura.lechuga@cin2.es introducing a single-mode recombination section [10]. The first devices were implemented with optical fibers [11][12][13][14][15] and the principle was later transferred to photonic crystal fibers [16,17] and integrated optics, as in the case of the bimodal waveguide (BiMW) device [18] developed by our group, where two transverse modes of different orders propagate in the same straight waveguide.
However, despite the wide range of geometries and configurations that have been presented, a full applicability of interferometric biosensors is still missing, mainly due to the complex readout of the interferometric response. The sinusoidal dependence of the output intensity introduces ambiguities for a clear evaluation of the sensor response, referred to as fringe order ambiguities, direction ambiguity, and sensitivity fading.
In order to overcome the drawbacks of the periodic readout, several approaches have been suggested to translate the standard interferometric detection scheme into an unambiguous linear phase evaluation. These approaches are mainly based on phase compensation or modulation techniques, introduced through different principles such as electro-optic [19][20][21], thermo-optic [22], magneto-optic [23], liquid crystals [24], or photosensitive layers [25]. More recently a coherent detection scheme was proposed by Halir et al. [26] to unambiguously extract the phase signal from an integrated Mach-Zehnder interferometer (MZI) modified with a three-waveguide output coupler. Other strategies to overcome these limitations rely on spectral interrogation [17,[27][28][29][30], where a shift of the interference pattern occurs in response to a refractive index variation, similarly to the working principle of optical resonators [31]. But for any of these approaches to be implemented, additional fabrication processes or bulky equipment, such as tunable lasers or spectrometers, are required to achieve a linear phase readout.
We recently introduced a simple and cost-effective phase modulation technique which does not require any additional fabrication processes or external equipment. This technique, previously applied to MZI geometry [32], employs a periodic modulation of the incident wavelength, achieved with common laser diodes, and Fourier deconvolution of the modulated signal to retrieve the phase information.
In this work our main goal is to demonstrate the validity of the method for all modal interferometers by considering two generic modes in a mathematical model. The method can then be directly applied to a specific device by assessing the dispersion relations of the modes of interest, which are determined by the configuration, materials, wavelength, and polarization. Here we chose a silicon-based single-path interferometer, the BiMW device, as a model case where two transverse modes of different orders are involved. In Section 2, the working principle of modal interferometers is presented, including the limitations of traditional monochromatic interrogation and the critical effects arising from spectral interrogation. Then, in Section 3, the mathematical modeling of the wavelength modulation approach is described for a generic interferometric output. Section 4 details the experimental implementation and the bulk calibration of the wavelength-modulated BiMW, along with a biosensing proof-of-concept through the detection of the C-reactive protein using a direct immunoassay.

Sensor working principle
The BiMW interferometer is constituted of a single-mode input waveguide followed by a thicker waveguide where two modes of different orders (fundamental and first order) propagate to the end of the device [18]. Due to their different confinement factors, the first-order mode is mainly responsible for the sensing of changes occurring on the device surface while the fundamental mode can be considered as a virtual reference.
A schematic view of the device is shown in Fig. 1. To ensure single-mode behavior in the longitudinal direction in the visible, a nanometric height rib waveguide (4 μm width × 1.5 nm height) is defined over a Si 3 N 4 core layer (150 nm for the single-mode section and 300-350 nm for the bimodal part) embedded between two SiO 2 cladding layers (1.5 μm thickness). In the bimodal section, a portion of the cladding is removed, defining a sensing area where the evanescent field of the guided light can probe the environment. Considering the propagation over a length L, the phase difference between the two modes is given by where N 0 and N 1 are the effective refractive indices of the two propagating modes, respectively, N eff their difference, and λ the working wavelength. Equation (2) is the general expression of the phase difference between the two propagating modes in any interferometer (double-and single-path), independently of the readout scheme (intensity or far-field distribution detection).
In the case of BiMW, the superposition of the two modes at the device output results in a two-lobe intensity distribution that depends on the phase difference accumulated across the whole bimodal length. The temporal evolution of this phase difference is quantified by the monitoring of the signal S R , given by where I up and I down are the currents measured by the upper and lower sections respectively of a two-section photodiode and V is the visibility factor. V represents the amplitude of the output variations (fringe amplitude) and it is determined by the coupling coefficients which govern the mode power splitting taking place at the step junction. In the monochromatic approach, we experimentally obtain visibility factors in the range 50-70% depending on the bimodal core thicknesses (300-350 nm) and on the working wavelength (600-700 nm). As S R is normalized to the total power propagating in the structure, it is immune to input fluctuations due to laser or mechanical instabilities, preventing false-positive responses.
As the phase variation is deduced from the variations of S R , the device sensitivity to refractive index changes is given by As shown in Fig. 2, the curves of the phase sensitivity ∂ ϕ/∂n computed from Eq. (2) as a function of the bimodal core thickness for a sensing area length L SA = 15 mm and a working wavelength λ 0 = 660 nm show maximum values for core thicknesses of 310 nm for TE polarization and 375 nm for TM polarization, corresponding respectively to 2510 × 2π and 3270 × 2π rad/RIU.
It should be noted that the device sensitivity expressed by Eq. (4) is slightly lower than the calculated phase sensitivity due to the presence of the term ∂ S R /∂ ϕ ∝ V sin( ϕ) which depends on the visibility V of the fringe pattern and on the initial value of the phase difference between the two propagating modes. This dependence of the sensitivity on the phase difference value, referred to as sensitivity fading, constitutes one of the main limitations of www.lpr-journal.org  the traditional intensity interrogation scheme. This drawback can be overcome by introducing alternative readout schemes, as demonstrated in this work. A sinusoidal dependence is generally assumed between the phase variation and the wavelength; however, due to the different relations of dispersion of the involved modes, a critical point can arise when the function N eff (λ)/λ shows an extremum [33]. As a consequence, the sensitivity of spectrally interrogated interferometric sensors diverges in proximity of the critical point rendering potentially ultrahigh-sensitivity detections, limited only by the system noise [17,33]. Figure 3 a shows the behavior of the function N eff (λ)/λ in the case of the BiMW device, with a bimodal core thickness of 340 nm and TE polarization. The curves are computed through two-dimensional simulations of the device cross-section, considering two different cases for the medium in contact with the sensing area. In the first case the medium is a silicon dioxide cladding (n = 1.46), resulting in a critical wavelength of around 665 nm (black curve), while in the case of water medium (n = 1.33) the critical wavelength is shifted to 685 nm (red curve). To assess the effective critical wavelength of the device, the propagation along the complete structure is computed and the resulting transmission curve S R is shown in Fig. 3  It should be mentioned that during our studies we found that the rib dimensions, crucial for single-mode lateral behavior, do not lead to substantial variations for the critical effects, the core thickness being the dominant parameter.
Because they are a consequence of modal dispersion, critical effects are more evident for single-path interferometers than for standard two-path configurations where the same order dispersion relation governs both sensing and reference modes and the phase accumulation only takes place in the sensing area.
In the frame of intensity interrogation, i.e. constant wavelength, it is more convenient to study the critical behavior in terms of critical thickness for a given working wavelength. In the case of the BiMW sensor operated at 660 nm, the critical thickness is found to be around 330 nm. Out of the critical range, a sinusoidal dependence can be assumed for small wavelength variations.

All-optical phase modulation method
In order to solve the problems of the periodic sensor response and the resulting phase ambiguities, a modification of the phase difference between the two propagating modes can be introduced by altering their effective indices through small variations of the propagating wavelength. If this variation is introduced in a periodic manner, Fourier transform deconvolution can be applied, allowing one to directly access the phase information and furthermore to filter out noise contributions at a frequency different from the modulation frequency and its harmonics. Under the hypothesis of sinusoidal phase modulation f (ω) = μ sin(ωt) applied to a sinusoidal transfer function S( ϕ), we obtain a modulated output signal of the type where ω is the modulation frequency and μ the modulation depth. In the Fourier domain, the signal harmonics are given by where J n (μ) is a Bessel function of the first kind of order n, the amplitude of which depends on the modulation depth. The phase shift information can therefore be directly and unambiguously retrieved from the expression if J 2n+1 (μ) = J 2n (μ) .
With our approach, the sensitivity fading is solved since the phase information is retrieved from two signal harmonics of different order, I 2n and I 2n+1 , which show dependence on the phase difference, ϕ, of the type cos( ϕ) and sin( ϕ), respectively. Their sensitivities will therefore show alternated maxima and minima, which compensate each other along the phase variation.
For our application we chose the harmonics pair I 2 and I 3 since the low modulation depth required to satisfy Eq. (9), verified for μ = 1.2π , can be easily introduced experimentally.
In the context of the proposed all-optical modulation scheme, the theoretical phase modulation depth μ must be related to a particular wavelength shift λ M of the laser diode, which depends on the specific interferometer geometry, the constituent materials, and the working wavelength through the mode dispersion relations. For any device section of arbitrary length L, the variation of the phase difference between the propagating modes δ( ϕ) induced by a small change δλ of the propagating wavelength can be obtained by differentiating the general phase expression (2).
By making explicit the required wavelength change as a function of the induced phase shift we obtain which is the general equation valid for any modal interferometer once the mode nature is specified through N eff and the geometry by L. In the case of dual-path interferometers operating far from the critical point, as in our previous study [32], as the two modes of interest have the same order dispersion relation, the term ∂ N eff /∂λ can be neglected, resulting in simplified expressions of Eq. (10). However, considering the complete expression of Eq. (10), critical effects can appear as a consequence of the spectral interrogation when the denominator equals zero. For the BiMW geometry, the contributions of Eq. (10) from the three sections L in , L SA , and L fin (see Fig. 1) must be taken into account. The resulting modulation depth λ M required to satisfy Eq. (9) and to achieve phase linearization when a water medium is present in the sensing area is shown in Fig. 4 for the case of TE polarization and a central wavelength λ 0 = 660 nm.
As we can observe, the required modulation amplitude diverges in correspondence of the critical thickness (t ≈ 330 nm for λ 0 = 660 nm). Similar behavior is observed for TM polarization. In this case the divergence of the required modulation depth is observed for a thickness t ≈ 410 nm (data not shown). Taking into account the limited operation range of the laser diode (approximately ±0.5 nm), we can set boundaries which determine three regions: (i) sensor chips with bimodal part thickness lower than the critical value, (ii) sensor chips with waveguide thickness around the critical point, and (iii) sensor chips with waveguide thickness above the critical point. Sensor chips from family (ii) cannot be modulated with the proposed method: the required modulation depth diverges and cannot be introduced with our experimental approach. Sensor chips from families (i) and (iii) can be modulated www.lpr-journal.org and will show opposite directions for the phase variation in response to the same index change, due to the different signs of the required modulation depth. This change in the sensor response direction is in agreement with previous studies with hetero-modal fiber sensors [34,35] which showed a similar critical behavior for a given wavelength.
For an optimized sensor design, the bimodal core thickness is chosen by considering sensitivity maximization and the applicability of the wavelength modulation approach. In the following we experimentally study the behavior of sensor chips belonging to the three different regions of Fig. 4.

Experimental implementation
The sensor chip is placed over a custom-made, temperaturecontrolled chuck (T-resolution = 0.01 • C). End-fire coupling of polarized light from a fiber pigtailed laser diode (LP660SF60, λ 0 = 660 nm, Thorlabs) with controlled temperature and current is achieved by employing a three-axis stage platform. An optical isolator is used to protect the laser cavity from unwanted reflections and to select the polarization. For this experiment, TE polarization is considered. A two-section detector is directly anchored in proximity of the waveguide output through a customized holder. Its vertical position is adjusted to ensure a symmetric S R pattern (i.e. centered around zero) and maximum visibility. The intensity signals are amplified by commercial photodiode amplifiers, recorded with an acquisition card, and processed in real time.
For optical characterization a modulation frequency of 214 Hz is adopted since it allows one to resolve the changes of interest (time scale of minutes) and it is not affected by hardware limitations.
The theoretical requirements of the wavelength modulation depth are experimentally transferred to a condition on the amplitude of the laser driving current oscillations. A wavelength shift of 0.5 nm can be introduced with current variations around ±50 mA, which can usually be achieved by commercial laser diodes.
A custom-made Labview application is used for the generation of the input modulation signal and for the data acquisition process, synchronous with the input. A fast Fourier transform of the modulated output is computed in real time and the phase signal is evaluated from Eq. (8): the second and third harmonics are extracted from the real and imaginary portions of the Fourier spectrum respectively. After an unwrapping step to remove the 2π discontinuities, a continuous and monotonic signal is obtained in real time. As the BiMW output is normalized to the total power, there is no need for a reference signal to compensate for the amplitude modulation effects introduced by varying the laser driving current.
The deviations of the laser emission from an ideal case of perfect linear dependence on driving current and slight fabrication variations are overcome with a pre-set of the working point: the amplitude of the laser current oscillations is varied until the acquired harmonics oscillate in the same range, satisfying Eq. (9). Figure 5 shows a comparison of the harmonic behavior during a variation of the refractive index in the sensing area for a sensor chip of family (i) modulated with a laser current amplitude I LD = ±28 mA and a sensor chip of family (ii) modulated with a current variation I LD = ±67 mA. It can be noted how in the case of chip (i), operated at the correct working point, the second and third harmonics oscillate in the same range, while for chip (ii), despite the use of the maximum current excursion allowed, the amplitude of the oscillations of the second harmonic is larger than that of the third one. For this last chip the working point cannot be experimentally reached due to the divergence of the required modulation depth (compare Fig. 4). For a given configuration, the critical region can be circumvented by modifying the central wavelength or the polarization of the incident beam. For instance, the chip of family (ii) could be modulated in TM polarization as in this case the critical region would be shifted to longer wavelengths.

Bulk sensing evaluation
For the demonstration of the phase modulation technique we chose two sensor chips with different core thicknesses: one belonging to group (i), with core thickness lower than the critical value; one belonging to group (iii), with core thickness higher than the critical value.
For the evaluation of the bulk refractive index sensitivity, different solutions of hydrochloric acid are sequentially supplied to the sensors through a fluidic system, while Milli-Q water is used as running buffer. A custommade methacrylate cell with embedded polydimethylsiloxane channels allows access to a specific sensor in the chip, while a syringe pump maintains a constant flow regime. The refractive indices of the solutions are determined previously with an Abbe refractometer.
The insets in Fig. 6 show the temporal evolution of the sensor response when supplying different HCl solutions for  Fig. 6. Experimental sensitivities are evaluated from the linear fit shown in Fig. 6, resulting in values of 2120 × 2π rad/RIU for sensor chip (i) and 1790 × 2π rad/RIU for sensor chip (iii), in agreement with the theoretical modeling. The experimentally measured sensitivities correspond to the device sensitivity expressed by Eq. (4) and are therefore slightly lower than the phase sensitivities presented in Fig. 2.
The limits of detection are evaluated assuming that the smallest detectable signal corresponds to three times the standard deviation on the baseline signal. Having standard deviations of 1.42 mrad for chip (i) and 2.45 mrad for chip (iii), we obtained limits of detection of 4 × 10 −7 and 5.7 × 10 −7 RIU for chips (i) and (iii) respectively. These values are comparable with the results achieved in the standard monochromatic approach employing a He-Ne laser [18], demonstrating the validity of the all-optical modulation method implemented with a standard laser diode.

Biosensing evaluation
For the validation of the wavelength-modulated BiMW as a biosensor we quantified the immunoreaction between the C-reactive protein (CRP) and its monoclonal antibody (C7 antibody), previously immobilized on the sensor chip surface. CRP is a cyclic pentameric protein produced by the liver, the concentration of which dramatically increases in the presence of inflammation or infections. It has been related to hypertension and cardiovascular diseases [36,37], and is one of the biomarkers rapidly evaluated in healthcare emergency units for any new incomer. The assay is implemented on the sensor chip from family (i), the most sensitive of the two sensor chips previously characterized in bulk.
Prior to antibody immobilization, the silicon nitride surface of the sensor is hydroxylated to expose -OH groups on the surface and silanized with a water-soluble silane, carboxyethylsilanetriol sodium salt, following the protocol detailed by González-Guerrero et al. [38]. The use of silanes as bridge elements between silicon-based transducers and biological molecules is well established since a stable covalent immobilization of specific bioreceptors occurs [1,39]. The carboxylate groups are activated by 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide hydrochloride/Nhydroxysuccinimide agents, allowing the covalent anchoring of the antibody, which is done in situ and monitored in real time. The specific antibody is supplied to the sensor surface, at a concentration of 20 μg/ml. A 1 M solution of ethanolamine (pH = 8.5) is used as blocking agent to deactivate unreacted carboxylic groups and prevent non-specific absorptions. After stabilization of the bio-layer in phosphatebuffered saline (PBS) buffer, known concentrations of CRP diluted in PBS buffer in the range 10-500 ng/ml are supplied to the sensor, in a volume of 250 μl. The corresponding sensorgrams are shown in the inset of Fig. 7. Regeneration of the bioreceptor layer after CRP immunodetection is done with 10 mM hydrochloric acid.
A control experiment is done by injecting a non-specific protein sample containing human chorionic gonadotropin hormone at a concentration of 1 μg/ml, giving no appreciable signal, as demonstrated in the inset of Fig. 7.
From the data of the dose-response curve of Fig. 7 the detection limit is estimated as 7 ng/ml considering this value as the concentration inducing a signal equal to three times the baseline noise. This value, obtained with a direct and label-free immunoassay, is comparable to that of more complicated assay formats implemented for the same CRP/anti-CRP pair in other biosensor devices such as a surface plasmon resonance sensor [40] or electrochemical sensor [41] and satisfies the requirements of clinical application.

Conclusion and outlook
We demonstrated theoretically and experimentally a simple and cost-effective method to obtain a real-time linear signal as output, valid for any modal interferometer. The method is developed for a generic interferometric output, independent of the interferometric arrangement (single or double path) and of the readout approach (intensity or far-field pattern detection), resulting in a general approach which is later applied to the case of a BiMW sensor, where two transverse modes of different order propagate along the structure.
Careful design of the sensor chips is mandatory in order to overcome the critical effects arising from the difference between the dispersion relations of the involved modes. In proximity of the critical point a trade-off between sensitivity maximization and feasibility of phase modulation is necessary. We demonstrated bulk detection limits of the order of 4 × 10 −7 RIU and we presented a biosensing proof-of-concept for the immunoassay of the inflammatory biomarker C-reactive protein.
For future designs of interferometric biosensors, we believe that this wavelength-based modulation approach can offer a valid solution for bypassing interferometric limitations without increasing the complexity of design, fabrication, and measuring procedures. This offers a competitive solution for the implementation of lab-on-a-chip platforms employing interferometric biosensors, which can be commercialized in the near future.